Mathematical Programming in the Oil Industry

The
oil industry is the largest single user of Mathematical Programming.
Why this should be so and how Mathematical Programming iss used are the
subject of this article.

Upstream and Downstream

The oil industry is normally divided into two parts:

upstream, concerned with finding oil deposits (exploration) and getting the crude oil out of the ground (production);

downstream, concerned with turning crude oil into usable
products (refining and petrochemicals) and delivering them to customers
(distribution).

Note
the use of the term "production". In most industries (e.g. making cars)
this is used where goods are manufactured. Not so the oil industry. It
follows the practice of other primary industries (e.g. mining) in using
"production" to refer to the process of obtaining the raw material. Oil
refining is a manufacturing process; indeed, some oil companies
use the term "manufacturing" to refer to both oil refining and
petrochemical manufacturing.

Exploration and Production

The
problems which face the upstream industry are essentially geological
and engineering. They must use available survey data to decide where to
drill exploratory wells and then interpret the results. They must
design and build oil platforms and production facilities which will
enable them to extract the available oil from the fields which they
discover. These are very challenging tasks which consume vast
quantities of highly-skilled effort. not to mention computing power.
But although the process of oil exploration has similarities to
fighting a war, little formal Operational Research is carried out.

Looking
at the specific OR technique of Mathematical Programming, one might
consider that problems would arise in finding the best way to use the
available resources of skilled manpower or finance. But this does not
appear to be so. Oil companies appear to be no better than others in
muddling through. It is true, also, that the oil industry has a highly
developed structure of service companies to whom tasks can be
contracted out. This is taken so far that some oil companies (but not
the majors) consist of little more than their top managements sitting
in an office.

Where
Mathematical Programming is used, it tends to be in relatively
specialised (and peripheral) areas such as logistics. An exception to
this was the suite of models which was developed by Scicon for the
Kuwait Oil Company (KOC). These were concerned with such fundamental
issues as deciding the daily oil production rate, which wells should be
used to achieve the day's production and planning the long-term
strategy for developing new fields.

Setting the Total Production Rate

The
problem which KOC faced in setting the day's production rate was
essentially one of trying to keep the production rate stable when the
quantity exported from day to day was volatile and there was only
limited buffer storage available. A single large oil tanker can carry
as much crude oil as Kuwait produces in a day. Tankers were scheduled
to arrive so that exports would match the production rate. But
inevitably there were fluctuations in the scheduled daily offtakes and
disruptions would also occur, for instance because of dust storms.

Some of
these fluctuations in daily offtake could be smoothed out by the use of
buffer storage tanks of crude oil. But these were of limited capacity
and it is a brave (and foolhardy) man who uses the entire buffer
capacity in the expectation that relief is at hand. The consequences of
exhausting the buffer were severe, ranging from disruption to the oil
fields through to incurring penalty payments to shipowners. The prudent
approach was therefore to modify the production rate as problems
emerged, but to do so in a highly damped way.

A
dynamic programming model was used to achieve this and determine the
day's production rate. This took account of the available information:
the stock levels, predicted tanker arrivals, local market demand, etc.
It balanced the conflicting factors and ensured that the production
rate moved modestly to anticipate problems rather than dramatically
once the problems had become severe.

Deciding Which Wells to Use

When an
oilfield is developed, detailed plans are drawn up of the most
efficient way to extract the available oil. Wells are then drilled and
extraction follows the plan. In the North Sea, wells are expensive to
drill and so all the wells which can contribute to oil extraction are
used. But in OPEC countries which are subject to an export quota, the
oil fields may have more wells than are needed to produce the required
quantity of oil. In such a case there is a selection problem to decide
from which wells the required production should be drawn.

KOC
used a Linear Programming model to tackle this selection problem. The
model represented the wells and the surface facilities which collect
the oil and process it, extracting the associated gas. Individual wells
differ from one another in the quality of the oil which they produce
and in the quantity and composition of the associated gas. The
principal variation is in the density of the oil and in the sulphur
content. There is a quality specification for the crude oil which
Kuwait exports and this gives rise to quality constraints on the
aggregate production from the wells. Other constraints relate to the
processing capacity of the surface facilities and engineering
considerations for the efficient production of the oil.

Oil Refining

It is
in the downstream oil industry, and in oil refining in particular, that
the use of Mathematical Programming is most widespread. This is because
the technique is effective in tackling the problems which the industry
faces.

It has
also been important that oil refineries are enormous businesses with an
annual turnover of as much as $1 billion each. With that scale of
operations, the costs of developing an MP model are repaid very
quickly. Indeed, so favourable are the economics that oil refineries
led the commercial development of Mathematical Programming in the 1960s
and 1970s.

Figure 1 gives a very simple representation of what happens in an oil refinery.

Figure 1: Schematic of an Oil Refinery

Crude
oil is subjected to fractional distillation in a Crude Distillation
Unit (CDU). This produces a series of intermediate products, the
quantities and qualities of which depend on the crude processed and the
processing conditions. Some of these intermediate components are then
subjected to further processing to make yet more intermediates. Finally
the intermediate components are blended together to make finished
products in accordance with quality specifications.

The characteristics of a typical MP problem are:

many potential solutions;

some measure of the quality of solutions;

interconnectedness between the variable elements of the system.

Oil refineries face an enormous number of options in their operations:

which crudes to refine;

what processing conditions to use;

which products to sell;

how to blend them from the intermediate components.

There
is a straightforward measure of the quality of the alternative
solutions: the profit (or value added) by the refinery's operations.
This measure is affected by all the decisions which are taken. The
prices of crudes and products vary from one to another, while the
quantities of finished products which can be made depend on the crudes
which are processed.

The
operations of the refinery are intrinsically interconnected: it is a
sequential process and choosing to process one crude means that you
have less processing capacity available for others.

Thus
the problems which a refinery faces have the characteristics of an MP
problem. But that does not mean that it is straightforward to apply MP.
In fact, the problem is not even a single problem at all: there is a
hierarchy of problems which oil companies face over a variety of scopes
- global, regional, single refinery, etc - and a variety of time
horizons - 5 years, 3 months, 1 week, etc. Different techniques are
used to tackle these separate aspects of the problem, as will be
explained in subsequent articles.

Petrochemicals

To
finish this survey, it is worth remarking why petrochemicals should be
such a small user of MP compared with oil refining. This is because
petrochemical plants are concerned with chemical reactions whereas oil
refineries are concerned primarily with physical processes (separation
and mixing). Chemical reactions take place between pure components in
specific ratios. The scope for varying what you are doing, whether
changing the feedstock or the process conditions, is marginal.

By
contrast, the physical reactions of an oil refinery split up various
cocktails of hydrocarbons (different crudes) and then reblend the
components to make new cocktails with lower variability (finished
products, e.g. petrol). Apart from some processes which chemically
alter the hydrocarbon molecules, the molecules which enter the refinery
in crude are the same molecules which leave it in the products.
Decisions have to be taken as to where the molecules go, and these
decisions give rise to a natural MP problem.